The area rule is an important concept related to the drag on an aircraft or other body in transonic and supersonic flight. The area rule was developed in the early 1950s when production fighter designs began pushing ever closer to the sound barrier. Designers had found that the drag on these aircraft increased substantially when the planes traveled near Mach 1, a phenomenon known as the transonic drag rise. The increase in drag is due to the formation of shock waves over portions of the vehicle, which typically begins around Mach 0.8. The drag increase reaches a maximum near Mach 1. Because the pressure drag increase results from the shock waves, this type of drag is referred to as wave drag.
Since the physics of supersonic flight were still largely a mystery to manufacturers, designers had no idea how to address this problem except to provide their aircraft with more powerful engines. Even though jet engine technology was rapidly advancing in those days, the first generation of jet-powered fighters was hampered by relatively low-thrust engines which limited them to subsonic flight. The US Air Force hoped to overcome this deficiency with its first dedicated supersonic fighter, the F-102 Delta Dagger.
Since the transonic drag rise was still not fully understood, the F-102's designers chose an engine they believed would provide enough thrust to reach a maximum speed of about Mach 1.2. However, initial flight tests of the YF-102 prototype indicated that the aircraft could not reach Mach 1. The aircraft's designers did not understand this lack of performance until a NACA researcher named Dr. Richard Whitcomb developed the area rule.
Whitcomb experimented with several different axisymmetric bodies and wing-body combinations in a transonic wind-tunnel. He discovered that the drag created on these shapes was directly related to the change in cross-sectional area of the vehicle from the nose to the tail. The shape itself was not as critical in the creation of drag, but the rate of change in that shape had the most significant effect. Stated differently, the wave drag is related to the second-derivative (or curvature) of the volume distribution of the vehicle.
To illustrate the point, Whitcomb's experimental models included (1) a simple cylindrical fuselage, (2) a cylindrical fuselage with wings attached, (3) a bulged fuselage, and (4) a “wasp-waisted” fuselage with wings. The addition of wings to the basic cylinder produced twice as much drag as the cylinder alone. Additionally, the drag rose by the same amount if a simple bulge was added to the cylinder, the bulge having equivalent volume to the wings. However, if the cross-sectional area of the fuselage was reduced over the region where the wings were attached, the total drag was about the same as that of the cylinder alone.
The conclusion of this research was that the drag on an aircraft could be drastically reduced by shaping the vehicle to create a smooth cross-sectional area distribution from the nose to the tail. The area rule dictates that the volume of the body should be reduced in the presence of a wing, tail surface, or other projection so that the discontinuities in the second derivatives of the total area distribution can be significantly reduced to match the distribution of a given minimum drag equivalent body.
Whitcomb's findings are related to a more theoretical concept called the Sears-Haack body. This shape yields the lowest possible wave drag for a given length, Mach number and volume. The variation in cross-sectional area for a Sears-Haack body results in minimized wave drag when the curvature of the volume distribution is minimized. The closer the volume distribution of an aircraft or other high-speed vehicle comes to the ideal Sears-Haack body, the lower its wave drag will be.
The area rule has found greater application to subsonic aircraft, particularly commercial airliners since they cruise at the lower end of the transonic regime. A good example is the Boeing 747, known for its distinctive “hump.” This hump, which houses the cockpit and upper passenger deck, increases the cross-sectional area of the forward fuselage and has the effect of evening the volume distribution over the length of the aircraft. As a result, the 747 is able to cruise efficiently at a slightly higher speed than most other airliners since the increase in transonic wave drag is delayed. It is very difficult, however, to achieve realistic vehicle configurations that completely meet the ideal Sears-Haack body.